You sure do like to fill paragraphs with baloney. None of what you said indicates how "The Induction StepAssume Q(m) is true for all m. That is, a group of m people is a party. Surely, removing a single person from a party will not alter it's party status. Thus, if Q(m) is true, then Q(m + 1) is true." is mathematically valid. Just because you say something "surely" doesn't make it mathematically valid. How can removing a single person from a party "surely" not alter its party status if we consider parties sized two or one or no people at all?

I'm not sure how else to describe a 20-post discussion about math pedantry. But if you're not trolling when you describe your "proof" as mathematically valid then I'd hate to see your real proofs. Math isn't just some game of mad libs; not only does the structure have to work but the arguments contained therein have to work as well.

What you probably wanted to say is "for some m". Q(m) being true for all m is what you want to prove at the first place.

Other than that, this indeed is a mathematically valid proof. The problem is in the statement "Surely, removing a single person from a party will not alter it's party status." Assuming that statement is true, the proof itself is correct.

The problem with a sand heap is that a sand heap has an infinite number of grains of sand in it, that's why an induction like this cannot work.

I've never heard of the sand heap in that paradox having an infinite number of grains, though; is that something I've just been missing? The reason the assumption-statement would be true (whether it be for a sand heap or a party) is because of the lack of definition for either. If one defined a party as "A gathering of 40 people," then removing a single person from a 40-person party would stop it from being a party (but then there'd be no Sorite's Paradox in the first place).

The paradox a bit more intuitive when one considers a heap of sand, but the same kind of definition can resolve it. Surely, removing a grain of sand from a heap of 1,000,000,000,000 grains does not make it not a heap. And, similarly, removing one more grain of sand does not. But, if we defined a "heap" as 999,999,999,998 grains or more, then removing a third grain of sand would make it not a heap.

Once you definitively define (!) things, there isn't much of a paradox.

So, the guy in the strip doesn't understand induction, and that's why he has no friends to come to his party? Maybe if you guys here could explain how it works to him, then he'd be better able to have friends.

I could not find that book anywhere. Would you mind posting a quote? (I am still fairly certain the Sorites Paradox does not require infinite grains of sand, but am curious of the author's purpose in using it for one—and about the claim that it requires an infinite number of grains for the other).